With the aid of automatic parking brakes, vehicles are immobilized at a standstill by generation of a continuous braking force. Parking brakes having an electric motor, whose displacement motion acts via a gear drive, for example a spindle drive, directly on the brake pistons at the wheel brakes, are known. The electric motors are usually dimensioned so that a vehicle can be held in zero-energy fashion on slopes of at least 20%. With electric motors of smaller dimensions, or on steeper slopes, a hydraulic braking apparatus is additionally actuated in order to elevate the clamping force to the value required to immobilize the vehicle.